Cluster synchronization of nonlinearly-coupled complex networks with nonidentical nodes and asymmetrical coupling matrix

Abstract

In this paper, we investigate the cluster synchronization problem for networks with nonlinearly coupled nonidentical dynamical systems and asymmetrical coupling matrix by using pinning control. We derive sufficient conditions for cluster synchronization for any initial values through a feedback scheme and propose an adaptive feedback algorithm that adjusts the coupling strength. Some numerical examples are then given to illustrate the theoretical results.

Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control

“…The control action is hence directly exerted only into pinned nodes and propagates to the uncontrolled nodes through the connections among the nodes [20]. Recently, pinning-control scheme has been generalized to investigate cluster synchronization problems for complex dynamical networks with identical or nonidentical nodes [10,[22][23][24][25][26][27][28]. In [10], by proposing an effective pinning-control scheme, cluster synchronization was concerned for community networks with or without delay.…”

“…In [23], cluster synchronization for directed community networks was addressed by constructing a local feedback control scheme and an adaptive pinning strategy imposed on partial communities. In [24], cluster synchronization for nonlinearly coupled complex networks with nonidentical nodes and asymmetrical coupling matrix was investigated under pinning control. Based on a decentralized adaptive pinning strategy, cluster synchronization of undirected complex dynamical networks was discussed in [25].…”

Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive control

“…Recently, combining impulsive control and linear feedback control, exponential synchronization of hybrid impulsive and switching dynamical networks with time delays was studied [27], but the considered time delays were constants. On the other hand, the state variables of nodes x i (t) could not be gotten easily, but the g(x i (t)) can be obtained without difficulties, that is to say, nonlinear case is more realistic [28,29]. However, to the best of our knowledge, the synchronization problem of nonlinearly coupled complex networks with hybrid time-varying delays under impulsive control, until now, receives few attentions.…”

Exponential Synchronization of Two Complex Dynamical Networks of Random Disturbance with Both Mixed Coupled and Time-Varying Delay by Pinning Control

“…It is a phenomenon that has been widely investigated since it was discovered by Pecora and Carroll in 1990 [8]. Many synchronization patterns have been explored (for example, complete synchronization [9][10][11], cluster synchronization [12,13], phase synchronization [14], partial synchronization [15], projective synchronization [16,17]), and synchronization can be achieved by the use of pinning control [18,19], adaptive control [20][21][22], intermittent control [23], impulsive control [24,25], fuzzy control [26], hybrid control [27] or active control [28].…”